Defining a shapefile's coordinate system by specifying a new projected coordinate system

Steps:

1. In ArcCatalog, click the shapefile whose coordinate system you want to define.
2. Click the File menu and click Properties.
3. Click the XY Coordinate System tab.
4. Click New and click Projected.
5. Type a name for the custom coordinate system.
6. Click the Projection Name drop-down arrow and click one of the supported projections.
7. Type the appropriate parameter values for the projection.
8. Click the Linear Unit drop-down arrow and click a predefined unit of measure.

   Alternatively, click <custom> in the drop-down list, type the appropriate meters per unit, then type a name for your custom units.

9. Define the projection's datum by selecting a predefined geographic coordinate system or defining a new geographic coordinate system. Afterward, you can modify the geographic coordinate system's parameters if you want.
10. Click OK.
11. Click OK on the Shapefile Properties dialog box.